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During the two years in which I have been engaged on this work, I have received from Teachers of Geometry in all parts of the country so much encouragement to proceed, and so much assistance at each step of my progress, that I feel justified in asserting that no text-book on Elementary Geometry is likely to meet with general support in England, if it involve any wide departure from the Euclidean model.
It only remains for me to offer my thanks to the friends who have improved this work by their advice, and to assure each reader of the book that any suggestion for its further improvement will be thankfully received by me.
J. HAMBLIN SMITH.
42 TRUMPINGTON STREET,
EUCLID'S PROPOSITIONS I. TO IV.
SECTION II.-ON THE THEORY OF PARALLEL LINES-Pp. 44 to 56.
EUCLID'S PROPOSITIONS XXVII. AND XXVIII.
Note 5. ON THE SIXTH POSTULATE
EUCLID'S ELEMENTS-BOOK V.
SECTION I.-ON MULTIPLES AND EQUIMULTIPLES-Pp. 211 to 214.
SECTION II.-ON RATIO AND PROPORTION-Pp. 215 to 229.